For “ Quadro : a Supervised Dimension Reduction Method via Rayleigh Quotient Optimization
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چکیده
Lemma A.1. If U follows a uniform distribution on Sd−1, for any d×d diagonal matrix S and any vector β ∈ Rd, we have • E(U>SU) = tr(S) d , E[(U >SU)2] = 2 tr(S 2)+[tr(S)]2 d2+2d ; • E(U>β) = 0, E[(U>β)2] = ‖β‖ 2 d ; • E(U>SUU>β) = 0. Now, we show the claim of Proposition 2.1. Let Y = Σ−1/2(Z −μ), then Y = ξU where U follows a uniform distribution on Sd−1 and is independent of ξ. The quadratic form Q(Z) can be rewritten as
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تاریخ انتشار 2014